As is known in the art, a typical ring binder retains loose leaf pages or document papers with hole-punched edges in a file or a notebook. The ring binder generally comprises an elongated housing, a pair of pivotable hinge plates located in the housing and clamped together by the housing, and half ring members fixed to the hinge plates. The housing is relatively highly rigid, but still has certain elasticity so that it can be slightly expanded in a transverse direction by the hinge plates. The hinge plates abut against each other at their inner edges and engage with transversely bent-in edges of the housing at their outer edges. The hinge plates are thus hinged to each other so that they can pivot relative to each other within a certain angle. Each of the hinge plates is fixed with the same number of half ring members at longitudinal locations corresponding to the holes punched along one edge of each of the stacked pages. The half ring members are closed or opened as the hinge plates pivoting. When closed, opposite half ring members provided at the same longitudinal locations on the two hinge plates respectively abut against each other by their tip ends, forming a complete ring for retaining loose-leaf pages. When opened, the tip ends of the opposite half ring members are separated from each other to form an opening therebetween through which loose-leaf pages can be taken out or loaded into the binder. The rings formed by the half ring members in a traditional binder typically have circular, arc, rectangular or other shapes. When the rings have circular, arc or other curved main bodies, the hole-punched edges of the retained pages will follow the curved shape of the half ring members. Thus, the hole-punched edges of the pages cannot align with each other tidily in either open position or closed position. On the other hand, when the rings have rectangular or other straight main bodies, it is difficult to move the pages smoothly when loading them onto the rings or turning them along the rings. When a stack of pages are loaded or turned, they may be jammed or blocked on the rings. Accordingly, there is a need for a ring binder which allows the pages to be tidily aligned with each other and can be loaded and turned smoothly.